参数多面体的解析延拓与跨壁
Analytic continuation of a parametric polytope and wall-crossing
摘要：
定义了由不等式定义的多面体的集合论“解析延拓“。对于常规的参数值，我们的建设符合平行运输的多面体在海市蜃楼介绍了Varchenko。我们确定了集理论的变化时，跨越墙壁的参数空间，我们与这种变化的Paradan的跨墙公式的积分和离散和。作为另一个应用，我们改进了Brion定理关于多面体及其顶点锥的生成函数。我们描述了这一工作与环面簇上的线丛的等变指数和Morelli可构造的支撑函数的关系。
英文摘要：
We define a set theoretic "analytic continuation" of a polytope defined by inequalities. For the regular values of the parameter, our construction coincides with the parallel transport of polytopes in a mirage introduced by Varchenko. We determine the set-theoretic variation when crossing a wall in the parameter space, and we relate this variation to Paradan's wall-crossing formulas for integrals and discrete sums. As another application, we refine the theorem of Brion on generating functions of polytopes and their cones at vertices. We describe the relation of this work with the equivariant index of a line bundle over a toric variety and Morelli constructible support function.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
